Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
640 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 338 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#10587544 | C2 | direct (N × H) |
| 11. #10587544 | C22 | direct (N × H) |
| 15. C22×Dic17 | C8 | semidirect |
| 32. C2×Dic17 | C2×C8 | semidirect |
| 40. C22×C17 | C4⋊C8 | semidirect |
| 47. Dic17 | C22×C8 | semidirect |
| 53. C2×C17 | C2×C4⋊C8 | semidirect |
| 65. C17 | C22×C4⋊C8 | semidirect |
| 93. C22 | #10587544 | direct (N × H) |
| 103. C2 | C2×#10587544 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3624 | 2 |
| C2×#10587544 | 2 |
| C22×C4×Dic17 | 2 |
| C22×C4⋊C8 | 17 |